具有小修和一般型更换策略的多状态退化系统的定性分析  

Stability Analysis of a Multi-State Deteriorating System with Minimal Repairs and the Replacement Policy in General Distribution

作　　者：祁雪萍 阿不都克热木·阿吉[1] QI Xueping;ABDUKERIM Haji(College of Mathematics and Systems Science,Xinjiang University,Urumqi 830046)

机构地区：[1]新疆大学数学与系统科学学院,乌鲁木齐830046

出　　处：《系统科学与数学》2021年第9期2571-2594,共24页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(11761066)资助课题。

摘　　要：文章研究具有小修和一般型更换策略的多状态退化系统,该系统由2n+1个带有边界条件的微积分方程表示.运用C;-半群理论及算子理论证明该系统非负动态解的存在唯一性.并通过对系统算子谱特征的研究证明该系统的动态解强收敛于其稳态解.进一步利用共尾及豫解正算子的相关理论证明该系统的指数稳定性.In this paper,we investigate a multi-state deteriorating system with minimal repairs and the replacement policy in general distribution,which is described by 2 n+1 differential-integral equations with boundary conditions.By using the Cosemigroup theory and the operator theory,we prove the existence of a unique positive dynamic solution.And then,by analyzing the spectral characteristics of the system operator,we prove the dynamic solution of the system converges strongly to its steady-state solution.Furthermore,by using the theory of cofinal and resolvent positive operator,we prove the exponential stability of the system.

关 键 词：退化系统 C -半群理论 动态解 稳态解 指数稳定性 

分 类 号：O213.2[理学—概率论与数理统计]